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The MCTM Elementary Math Contest Who

Participates and Who Wins?

- Dr. David Ashley, dia059_at_smsu.edu

math.smsu.edu/faculty/ashley.html - Dr. Lynda Plymate, lsm953f_at_smsu.edu
- math.smsu.edu/lynda

Department of Mathematics Southwest Missouri

State University Springfield, MO 65804

Test Background

- MCTM Annual Exam
- 25 Regional Sites
- Grades 4,5, and 6
- Schools Select Participants 3-5/Grade Level
- Concepts Exam (24)Problem Solving (18)
- Exams measure conceptual understanding and

problem solving ability. - The top three winners go to State.

Research Design/Methodology

- Regional survey (10 Items)
- Parent Survey (30 Items)
- Exam Analysis
- Concept/Problem Solving
- Conceptual/ Procedural
- NCTM Content Standards

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Who Participated in 2004?

- 2783 Contestants at 25 Sites
- 4th Grade 956 students
- 5th Grade 939 students
- 6th Grade 888 students
- 388 State Finalists
- 4th Grade 127 students
- 5th Grade 132 students
- 6th Grade 129 students

Regional Test Results

State Finals Test Results

Regional Data Survey Results

Regional Data Survey Results

Regional Data Survey Results

Informal Findings

- From our parent survey, we found that there were

no significant differences on how males and

females were selected for the contest (57 took

preliminary tests) or prepared for the contest

(75 spent 5-20 hours working with teachers,

other students and family members). - In all categories and on both regional and state

exams, male participants outperformed (sometimes

significantly) female participants.

Participants By Gender

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Compare Gender Performance

Looking at the Exam Content

- Compare performance between concept and problem

solving abilities. - Compare performance between conceptual (rich in

relationships) and procedural (rules and

language) knowledge (Hiebert, 1986). - Compare performance between the 5 NCTM Content

Standards.

Concepts vs. Problem Solving

- Concept exams were 2/3 concepts and 1/3

problem solving. - Ex. If a given square has a side 8 inches in

length and you have to draw a square with four

times the area of the given square, how many

inches are in the length of a side of the square

you have to draw?

Concepts vs. Problem Solving

- Problem solving exams were 3/4 problem solving

and 1/4 concepts. - Ex. Four boys work together painting houses for

the summer. For each house they get 256. If

they work four months and their expenses are 152

per month, how many houses must they paint for

each of them to have a 1000 at the end of the

summer?

- Regional exams Students averaged 59 correct on

problem solving and 42 correct on concepts. - State exams This reversed, with 48 correct on

concepts and 38 correct on problem solving.

Conceptual vs. Procedural Knowledge

- Both regional and state tests had a higher

percent of conceptual questions (59, 65). - Regional exams Students did better on the

procedural (47 correct) than conceptual

(39 correct) questions. - State exams Performed on both was about 40

correct, with slight improvement by grade level

(4th - 35, 5th - 43, and 6 - 53 correct). - No significant differences between genders.

Mathematical Content in Exams

- Number/Operation Reg (37), State (28).
- Ex. Find the number of minutes in the month of

March. - Algebra/Thinking Reg (21), State (28)
- Ex. Two small pizzas and one large pizza cost

the same as five small pizzas. If a small pizza

costs 4, then what does a large pizza cost?

- Geometry Regional (14), State (16)
- Ex. The mid-points of a square are joined as

shown. A fraction of the original square is

shaded. What fractional part of the original

square is shaded?

- Measurement Regional (20), State (23)
- Ex. Cheryl is mowing the football field. It is

100 yards long and 75 feet wide. What is the

area of this football field in square feet? - Data/Probability Reg (8), State (6)
- Ex. The average monthly rainfall for 6 months

was 28.5 inches. If it had rained 1 inch more

each month, what would the average have been?

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Hardest Problems on Regional Exams

- 2/3 of them were concepts, not problem solving.
- Example How could you rewrite 12 x 5 12 x 8,

using the distributive property? - 71 measured conceptual knowledge.
- Example If x is an odd number, how would you

represent the odd number following it? - Number/operation and measurement were again the

content of the hardest questions. - Example If the area of a 1 x 3 rectangle is

increased by a factor of 16, what are all of the

possible whole-number dimensions of the new

rectangle?

Gender Issues Concerning Content

- 6th grade females had more success with number

and operation (93.8) on the regional concepts

test than males (59.2). For all other tests and

content areas, females scored slightly lower than

males.

Procedural Problem Solving (Females Shine) vs.

Creative Problem Solving (Males Shine)

- A square piece of paper is folded in half along

the diagonal. The area of the resulting triangle

is 50 cm2. What was the perimeter of the

original square? - What is the smallest possible sum for all

Wednesday dates in a 30-day month?

Questions Where Females Outperformed Males

- The following diagram represents what division

fact? - Your teacher tells you to turn to the facing

pages which sum to 405. To which pages do you

turn? - A 15 minute tape in an answering machine can

record how many 18 second messages?

Questions Where Females Outperformed Males

- Mad King Ludwig had a castle with a moat around

it. One could enter the castle yard over 3

different drawbridges. From the castle yard, one

could enter the castle through 4 different gates.

There were 5 different doors through which one

could enter the throne room. How many different

ways from outside the castle could one enter the

throne room? - Tyrel gave Tonisha half of his Pokemons. Tonisha

gave half of these to Erin. Erin kept 8 of them

and gave the remaining 10 to Seri. How many

Pokemons did Tyrel give to Tonisha?

Questions Where Males Outperformed Females

- 2/3 of them were problem solving, not concepts.
- Example What is the smallest positive whole

number answer possible when you rearrange the

following seven symbols, using each exactly once?

( x - ) 9 2 4 - There was an even split between conceptual and

procedural knowledge. - 36 of them involved numbers/operations, and

another 27 of them involved measurement. - Example Find the distance between the two

points (3, 5) and (6, 4).

Gender Differences Involving Repeaters

- For both 5th and 6th grade regional contests, the

percent of repeating male participants (38, 43)

was higher than female repeaters (33, 38). - 40 of both 5th and 6th grade state qualifiers

had also qualified for state the previous year

(45 males, 30 females). 40 of 6th grade state

qualifiers had also qualified for state 2 years

previous (43 male, 32 female).

Possible Reasons From Literature Review For

Gender Differences

- The dominance of males in mathematical contests

can discourage females from pursuing their

interest in the subject. - By the second grade students have already

identified math and science as male. - By third grade, females rated their own

competence in mathematics lower than that of

their male classmates, even when they received

the same or better grades.

Possible Reasons From Literature Review For

Gender Differences

- Young females gain less experience than males

with core math concepts due to the kinds of toys

geared toward each gender. - From birth, female infants are discouraged from

risk-taking and from exploring the world around

them, whereas males are given toys that encourage

small motor skills and spatial visualization

skills, both necessary for later development in

mathematics. - The preferred learning style for females is

working collaboratively rather than

competitively, and that females would enjoy

mathematics more and increase their time on task

if it were taught in a cooperative setting.

Possible Reasons From Literature Review For

Gender Differences

- Self-confidence (or lack thereof) may also be a

strong contributing factor to why males are

outperforming females on this contest. - The mathematics curriculum at middle school

emphasizes abstract concepts and spatial

visualization, two skills that many females have

not had much experience with in pre-school and

primary levels. - Studies point to parental and societal

perceptions and teacher behavior and expectations

as the main reasons that females select out of

science and mathematics.

Sample Questions By Content Standard

Number/Operation

- Put the following problems in order (listing the

letter for each) according to the size of their

answers, smallest first - 49.95 X 70
- 2.49 X 99.9
- 9.99 X 499
- 99.9 X 9.80099
- David has 500 in a savings account. If his

money earns 6 interest at the end of each year,

how much money will he have in total after

collecting his interest for the 6th year?

Sample Questions By Content Standard

Algebra/Algebraic Thinking

- If you multiply a one-digit number by 3, add 8,

divide by 2, and subtract 6, you will get the

number you started with back. What is the

number? - 0 gt 2.
- 1 gt 4.
- 3 gt 8.
- 5 gt 12 If the same rule applied to every

number, then 6 gt ? . - What temperature in Fahrenheit is equivalent to

35 degrees Centigrade?

Sample Questions By Content StandardGeometry

- Thirteen one-inch cubes are put together to form

the T-figure below. The complete outside of the

T-figure (including the bottom) is painted red

and then separated into its individual cubes.

How many of the cubes have exactly 4 red faces? - Find the distance between the points (3,5) and

(6,4) to the nearest hundredth.

Sample Questions By Content StandardMeasurement

- Cheryl is mowing a ball field. It is 125 yards

long and 75 feet wide. What is the area of the

ball field in square feet? - When the circumference of a toy balloon is

increased from 20 inches to 25 inches, the radius

is increased by? - A model car has a scale in which 1/4 inch

represents 28 inches. If the completed model is

2 3/4 inches long, how long is the actual car?

Sample Questions By Content StandardData and

Probability

- A motorist drives through three sets of traffic

lights every day. The probability that the

motorist has to stop at the first set of lights

is 0.4, at the second 0.6, and at the third 0.63.

Each set of lights is independent of the others.

Calculate the probability that the motorist does

not have to stop at any of the lights. - What number should be added to the following set

of data so that the mean, median, and mode will

become the same number?

91, 93, 93, 95, 95, 98, 100

Reference list

- Ashley, David I. Plymate, Lynda (2004). Gender

Differences in the Missouri State Elementary Math

Contest. In the Missouri Journal of Mathematical

Sciences. Volume 16. Number 1. Winter 2004 pp 40

50. - Plymate, Lynda Ashley, David (2003).

Elementary Mathematics Contests Student

Performance on Questions Which Reflect NCTM

Standards. Teaching Children Mathematics. Vol.

10 Num. 3 Nov. pp 162-169.